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I'm numerically solving the ODE equation $a = -kv$, i.e. $ x'' = -kx'$.

sol = NDSolve[{y''[x] + 0.1 * y'[x] == 0, y[0] == 0, y'[0] == 10}, y, {x, 0, 100}]

I need to do plots of x versus time, v versus time, and v versus x. I figured out how to do the first two plots, but I'm having problems with plotting v versus x (i.e. y' versus y)

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You can try using ParametricPlot for that. – Leonid Shifrin Jan 24 '13 at 19:02
ParametricPlot[{y[t], y'[t]} /. sol[[1]], {t, 0, 100},  AspectRatio -> 1/2,
            PlotRange->FullAxesLabel -> {y[t], y'[t]}, LabelStyle -> Directive[20]]

Mathematica graphics

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